Abstract
The article deals with infinitary modal logic. We first discuss the difficulties related to the development of a satisfactory proof theory and then we show how to overcome these problems by introducing a labelled sequent calculus which is sound and complete with respect to Kripke semantics. We establish the structural properties of the system, namely admissibility of the structural rules and of the cut rule. Finally, we show how to embed common knowledge in the infinitary calculus and we discuss first-order extensions of infinitary modal logic.
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18 August 2022
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Acknowledgements
I wish to thank Pierluigi Minari and Mario Piazza for useful discussion on the topics of the present work. I am grateful to Sara Negri for helpful comments on an early version of the present paper.
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Tesi, M. On the Proof Theory of Infinitary Modal Logic. Stud Logica 110, 1349–1380 (2022). https://doi.org/10.1007/s11225-022-09998-x
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DOI: https://doi.org/10.1007/s11225-022-09998-x